Exercise

Question 5

Exactly, if Kobe has a hot hand, the probability that he makes his second shot would be higher, for example 0.60. As a result of these increased probabilities, you'd expect Kobe to have longer streaks. Compare this to the skeptical perspective where Kobe does not have a hot hand, where each shot is independent of the next. If he hits his first shot, the probability that he makes the second is still 0.45:
$$P(\mathrm{shot}_2=H~|~\mathrm{shot}_1=H) = 0.45.$$

In other words, making the first shot did nothing to effect the probability that he'd make his second shot. If Kobe's shots are independent, then he'd have the same probability of hitting every shot regardless of his past shots: 45%.

Now that we've phrased the situation in terms of independent shots, let's return to the question: how do we tell if Kobe's shooting streaks are long enough to indicate that he has hot hands? We can compare his streak lengths to someone without hot hands: an independent shooter. Starting with the next exercise, you'll learn how to simulate such an independent shooter in R.

If Kobe's shooting streaks diverge significantly from an independent shooter's streaks, we can conclude...